Before the switch to digital television broadcasting in 2009, many people withou

Question

Before the switch to digital television broadcasting in 2009, many people without cable or satellite had outdoor TV antennas. TV-antennas for VHF-Very High Frequency (channels 2 through 13) were made with perpendicular wires supported at their centers, as shown below. The ideal length for these wires is one-half the wavelength of the wave that is trying to be picked up, with the more expensive antennas having one for each channel. If you measure the lengths of the wires for channels 2 and 12 and find them to be 1.457 m and 0.207 m long, respectively. What is the frequency for channel 2? What is the frequency for channel 12?

Explanation / Answer

It is given that, the length of the antenna is the half of the wavelength to picked up.

For channel 2, the length is 1.457m

So the wavelength, 2 for the channel 2 is 2.914 m.

For channel 12, the length is 0.207m

And the wavelength, 12 for the channel 12 is 0.414 m.

Now we have,

= c

where,

is the wavelength

is the frequency

c is the speed of light

Therefore, frequency for channel 2 is,

2 = c/2 = 3 x 108 / 2.914 = 1.03 x 108 Hz

And frequency for channel 12 is,

12 = c/12 = 3 x 108 / 0.414 = 7.246 x 108 Hz

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